Swiss-Cheese Operad and Drinfeld Center

Najib Idrissi
In: Israel J. Math. (2017) 221.2, pp. 941–972.
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We build a model in groupoids for the Swiss-Cheese operad, based on parenthesized permutations and braids, and we relate algebras over this model to the classical description of algebras over the homology of the Swiss-Cheese operad. We extend our model to a rational model for the Swiss-Cheese operad, and we compare it to the model that we would get if the operad Swiss-Cheese were formal.